P h ys i c s
Quantum
Weirdness?
It’s all in
your mind
A new version of quantum theory
sweeps away the bizarre paradoxes
of the microscopic world. The cost?
Quantum information exists only
in your imagination
F
By Hans Christian von Baeyer
lawlessly accounting for the behavior of matter on
scales from the subatomic to the astronomical, quantum
mechanics is the most successful theory in all the physical
sciences. It is also the weirdest.
In the quantum realm, particles seem to be in two places at
once, information appears to travel faster than the speed of light,
and cats can be dead and alive at the same time. Physicists have
grappled with the quantum world’s apparent paradoxes for nine
decades, with little to show for their struggles. Unlike evolution
and cosmology, whose truths have been incorporated into the gen­
eral intellectual landscape, quantum theory is still considered
(even by many physicists) to be a bizarre anomaly, a powerful reci­
pe book for building gadgets but good for little else. The deep con­
fusion about the meaning of quantum theory will continue to add
46 Scientific American, June 2013
Photograph by Caleb Charland
June 2013, ScientificAmerican.com 47
fuel to the perception that the deep things it is so urgently try­
ing to tell us about our world are irrelevant to everyday life and
too weird to matter.
In 2001 a team of researchers began to develop a model that
either eliminates the quantum paradoxes or puts them in a less
troubling form. The model, known as Quantum Bayesianism,
or QBism for short, reimagines the entity that lies at the heart
of quantum weirdness—the wave function.
In the conventional view of quantum theory, an object such
as an electron is represented by its wave function, a mathemat­
ical expression that describes the object’s properties. If you
want to predict how the electron will behave, you calculate how
its wave function evolves in time. The result of the calculation
gives you the probability that the electron will have a certain
property (like being in one place and not another). But prob­
lems arise when physicists assume that a wave function is real.
QBism, which combines quantum theory with probability
theory, maintains that the wave function has no objective reali­
ty. Instead QBism portrays the wave function as a user’s manual,
a mathematical tool that an observer uses to make wiser deci­
sions about the surrounding world—the quantum world. Specif­
ically, the observer employs the wave function to assign his or
her personal belief that a quantum system will have a specific
property, realizing that the individual’s own choices and actions
affect the system in an inherently uncertain way. Another ob­­
server, using a wave function that describes the world as the
person sees it, may come to a completely different conclusion
about the same quantum system. One system—one event—can
have as many different wave functions as there are observers.
After observers have communicated with one another and mod­
ified their private wave functions to account for the newly
acquired knowledge, a coherent worldview emerges.
Seen this way, the wave function “may well be the most pow­
erful abstraction we have ever found,” says theoretical physicist
N. David Mermin of Cornell University, a recent convert to QBism.
THE UNREAL QUANTUM
The notion that the wave function isn’t real dates back to the
1930s and the writings of Niels Bohr, one of the founding
fathers of quantum mechanics. He considered it part of quan­
tum theory’s “purely symbolic” formalism—a computational
tool, no more. QBism is the first model to give mathematical
backbone to Bohr’s assertion. It melds quantum theory with
Bayesian statistics, a 200-year-old discipline that defines “prob­
ability” as something like “subjective belief.” Bayesian statistics
also gives formal mathematical rules for how to update one’s
subjective beliefs in light of new information. By interpreting
the wave function as a subjective belief and subject to revision
by the rules of Bayesian statistics, the mysterious paradoxes of
quantum mechanics vanish, QBism’s proponents say.
Hans Christian von Baeyer is a theoretical particle
physicist and Chancellor Professor emeritus at the College
of William and Mary, where he taught for 38 years. He is a
fellow of the American Physical Society, author of six
popular science books, and the recipient of the Science
Writing Award of the American Institute of Physics
(twice), a Westinghouse AAAS Writing Award, and a
National Magazine Award for essays and criticism.
Consider again the electron. We know that each time we
detect an electron, we find it in one particular location. But when
we’re not looking, the electron’s wave function can spread out,
representing the possibility that the electron is in many different
places at once. Now make a measurement again. You’ll find the
electron back in a particular location. According to the standard
way of thinking, the observation causes the wave function to
instantaneously “collapse” back to a single particular value.
Because the collapse happens everywhere at exactly the
same time, it seems to violate the principle of locality—the idea
that any change in an object must be caused by another object
in its immediate surroundings. This, in turn, leads to some of
the puzzles that Albert Einstein called “spooky action at a
distance.”
From the very birth of quantum mechanics, physicists saw
the collapse of the wave function as a paradoxical and deeply
disturbing feature of the theory. Its uneasy mysteries pushed
physicists to develop alternative versions of quantum mechan­
ics, with mixed success [see box on page 50].
Yet QBism says that there is no paradox. The wave function’s
collapse is just an observer suddenly and discontinuously revis­
ing his or her probability assignments based on new informa­
tion, in the same way that a doctor would revise a cancer
patient’s prognosis based on a new CT scan. The quantum sys­
tem hasn’t undergone some strange and inexplicable change;
the change is in the wave function, which is chosen by the
observer to encapsulate the person’s expectations.
We can apply this way of thinking to the famous paradox of
Schrödinger’s cat. Quantum physicist Erwin Schrödinger imag­
ined a sealed box with a live cat, a vial of poison and a radioac­
tive atom. The atom has a 50–50 chance of decaying within an
hour, according to the rules of quantum mechanics. If the atom
decays, a hammer will smash the vial and release the poison,
killing the cat. If it doesn’t, the cat lives.
Now run the experiment—but don’t look inside the box. After
an hour has gone by, traditional quantum theory would hold that
the atom’s wave function is in a superposition of two states—
decayed and not decayed. But because you haven’t yet observed
what is inside the box, the superposition extends further. The
in brief
Quantum mechanics is an incredibly successful theory
but one full of strange paradoxes. A recently developed
model called Quantum Bayesianism (or QBism) combines quantum theory with probability theory in an effort to eliminate the paradoxes or put them in a less
troubling form.
48 Scientific American, June 2013
QBism reimagines the entity at the heart of quantum
paradoxes—the wave function. Scientists use wave
functions to calculate the probability that a particle will
have a certain property, such as being in one place and
not another. But paradoxes arise when physicists assume that a wave function is real.
QBism maintains that the wave function is solely a
mathematical tool that an observer uses to assign his or
her personal belief that a quantum system will have a
specific property. In this conception, the wave function
does not exist in the world—rather it merely reflects an
individual’s subjective mental state.
hammer is also in a superposition, as is the
vial of poison. And most grotesquely, the
standard quantum-mechanical formalism
implies that the cat is in a superposition—
it is both alive and dead at the same time.
By insisting that the wave function is a
subjective property of the observer, rather
than an objective property of the cat in the
box, QBism eliminates the puzzle. The
theory says that of course the cat is either
alive or dead (and not both). Sure, its wave
function represents a superposition of
alive and dead, but a wave function is just
a description of the observer’s beliefs.
Asserting that the cat is truly both alive
and dead is akin to a baseball fan saying
that the Yankees are stuck in a superposi­
tion of both won and lost until he reads
the box score. It’s an absurdity, a megalo­
maniac’s delusion that one’s personal state
of mind makes the world come into being.
The hope is that by removing the par­
adoxes, QBism will help physicists home
in on the truly fundamental features of
quantum theory—whatever they turn
out to be—and “prevent them from wast­
ing their time asking silly questions
about illusory puzzles,” Mermin says.
THE TROUBLEMAKER
Thought Experiment
The Fix for Quantum Absurdity
To explore the difference between Quantum Bayesianism and the standard interpretation
of quantum mechanics, consider the famous example of Schrödinger’s cat. In the standard telling, a cat and a vial of poison are sealed in a box. A quantum event that happens
with a probability of 50 percent breaks (or does not break) the vial and kills (or does not
kill) the cat. Before an observer looks inside the box, the wave function describing the system is in a superposition of both “alive” and “dead” states, as is the cat itself. The observation collapses the cat into one state or another. In QBism, by contrast, the wave function
is merely a description of the observer’s mental state. The superposition applies to this
state, nothing more. The cat is either alive or dead; the observation reveals which.
Standard
interpretation:
Wave function
implies
cat is both
dead and
alive
QBism was born i n a short paper published
in January 2002 under the title “Quantum
Probabilities as Bayesian Probabilities,”
by Carlton M. Caves of the University of
New Mexico, Christopher A. Fuchs, then
at Bell Labs in Murray Hill, N.J., and Rue­
diger Schack of the University of London.
All three are experienced quantum infor­
mation theorists, and their respective affiliations with a physics
department, an industrial laboratory and a department of math­
ematics illustrate the interdisciplinary nature of their field.
In the intervening decade Fuchs moved to the Perimeter
Institute in Ontario and assumed the role of QBism’s chief
spokesperson. He is a compact Texan with a cheerful disposition
and a genial manner. A sandy-colored cowlick at his hairline
hints at his irrepressible, irreverent sense of humor. Colleagues
are not surprised when he opens an article with the words “In
this paper, I try to cause some good-natured trouble.”
The core of Fuchs’s style is the conviction that science is
quintessentially a communal activity and that profound insight
is won only through vigorous intellectual combat. He is a whirl­
wind of activity, lugging his laptop around the world in a beatup backpack, organizing conferences, chairing scientific ses­
sions and giving lectures at universities.
In this spirit, Fuchs has pioneered a new form of literature.
In 2011 Cambridge University Press published his e-mail corre­
spondence with scientists around the world in a 600-page tome
entitled Coming of Age with Quantum Information. A
s it chron­
icles the birth pangs of QBism, it offers a glimpse of how theo­
Illustrations by Anna-Kaisa Jormanainen
Quantum
Bayesianism:
Wave function
describes
mental state
only; cat
is either
dead or
alive
retical physics is created by real-life, warm-blooded human
beings, not the two-dimensional creatures of Wikipedia. The
book also documents Fuchs’s conviction, contrary to most sci­
entists, that philosophy matters, not only in the way in which it
influences physics but also in the manner in which it is
informed by the profound insights of physics—or should be.
POSSIBLE PROBABLES
Fuchs’s openness to philosophical concerns becomes clear when
you consider how QBism forces us to reconsider what is meant
by probability. Probability is like “time”: we know what it is,
until we are asked to define it. Sure, the 50 percent probability of
throwing heads with a fair coin implies something about 100
tosses, but how does that intuition help to make sense of the
proposition that “the probability of rain this evening is 60 per­
cent,” or President Barack Obama’s 55/45 assessment, before the
event, of the probability of success for the bin Laden operation?
Over the past three centuries two competing definitions of
probability have been developed, each with countless variants.
The modern, orthodox alternative, called frequentist probabili­
ty, defines an event’s probability as its relative frequency in a
June 2013, ScientificAmerican.com 49
q ua n t u m p h i l o s o p h y
Four Interpretations of Quantum Mechanics
What is really happening in the quantum world? S
cientists have offered about a dozen different interpretations of what the mathematical
formalism implies. Quantum Bayesianism is perhaps the most radical; these four alternatives are among the most popular.
The Copenhagen interpretation, developed
principally by Niels Bohr and Werner Heisenberg at
the former’s institute in Copen­hagen, is the orthodox
version of quantum mechanics. The measurable
properties of a system such as an atom are collectively called its
quantum state. The quantum state, in turn, is described either by
a matrix, which resembles a spreadsheet, or a formula called the
wave function, which represents a map of possibilities. Contact
with the real world is made by the Born rule, a recipe for obtaining
measurable probabilities for a given quantum state (and for which
Heisen­berg’s mentor Max Born received a Nobel Prize). During
a measurement an observer causes a collapse of the quantum
state into a new state that describes the actual outcome of the
experiment. The instant­aneous collapse implies that actions can
have effects that travel faster than light.
The guiding field interpretation. A num­
ber of physicists, including Albert Einstein for a while,
favored rewriting the mathematical apparatus of
quantum mechanics to include a real physical field
of force that controls the motion of a particle. Unfortunately, this
appealing image breaks down as soon as several particles, say N
of them, are involved. They do not move in our familiar threedimensional space but in an abstract space with 3N dimensions.
More troubling is the fact that the guiding field exerts an actionat-a-distance force, in which physical effects are transmitted
instantaneously over large distances.
series of trials. This number is claimed to be objective and verifi­
able, as well as directly applicable to scientific experiments. The
typical example is the coin toss: In a large number of throws,
about half will be heads, so the probability for finding heads is
approximately ½. (To avoid the vague words “large,” “about”
and “approximately,” the definition is refined to require an infi­
nite number of tosses, in which case the probability takes on its
exact value of ½. Unfortunately, the value also becomes unveri­
fiable at this point and thereby loses its claim to objectivity.)
Applying this definition to weather prediction, one might count
real or simulated weather patterns, but as far as President’s
Obama’s hunch is concerned, the frequency interpretation is
useless—the bin Laden mission was manifestly irreproducible.
The older point of view, Bayesian probability, is named after
18th-century English clergyman Thomas Bayes, whose ideas
were perfected and promulgated by French physicist PierreSimon Laplace. In contrast to frequentist probability, Bayesian
probability is subjective, a measurement of the d
egree of belief
that an event will occur. It is a numerical measure of how an
agent would bet on the outcome of the event. In simple cases
such as coin tosses, frequentist and Bayesian probabilities
agree. For the prediction of the weather or of the outcome of a
50 Scientific American, June 2013
The many-worlds interpretation. The most
direct way of avoiding the conundrum of quantum
state collapse is to eliminate it. This drastic move has
gathered many supporters in recent years. The manyworlds interpretation posits a single quantum state of the world,
which unfolds smoothly and predictably. When an experiment is
performed to ascertain which of two slits an electron traversed, for
example, the quantum state does not collapse onto one slit. Instead
the world actually splits into two branches. We, the observers of
the real world, reside on one branch and are unaware of the other.
Thus, the universe really branches out like a tree into a vast multi­
verse in which every possible outcome actually occurs in one of an
infinity of distinct, real universes. The principal drawbacks of this
interpretation, aside from its exorbitant demands on our imag­
ination, are its failure to account for the “measurements” that lead
to branching and its difficulty in justifying the Born rule.
Spontaneous collapse theories. R
ather than
eliminating the observer-triggered collapse, these
theories posit that collapses are entirely natural—
they happen spontaneously, though rarely, to every
quantum system but become significant when the quantum
system interacts with a macroscopic object. Yet they require the
invention of an entirely new mechanism of collapse. As long as the
collapse mechanism cannot be tested experimentally, it constitutes
a new assumption that is every bit as mysterious as the observerinduced collapse it is designed to replace.
military action, the Bayesian, unlike the frequentist, is at liber­
ty to combine quantitative statistical information with intui­
tive estimates based on previous experience.
The Bayesian interpretation easily deals with single cases,
about which frequentism is silent, and avoids the pitfalls of infin­
ity, but its real power is more specific. On the basis of this inter­
pretation, probability assignments are subject to change because
degrees of belief are not fixed. A weather forecaster who is a fre­
quentist would have no trouble calculating the likelihood of rain
if the region has had a stable, predictable climate for many years.
But in the case of a sudden change, such as a drought, for which
there are little data, a Bayesian forecaster is better equipped to
account for the new information and the climate condition.
Central to the theory is an explicit formula, called Bayes’ law,
for calculating the effect of new information on the estimate of a
probability. For example, when a patient is suspected of having
cancer, the physician assigns an initial probability, called the prior,
based on data such as the known incidence of the disease in the
general population, the patient’s family history, and other relevant
factors. On receiving the patient’s test results, the doctor then
updates this probability using Bayes’ law. The resulting number is
no more and no less than the doctor’s personal degree of belief.
Most physicists profess faith in frequentist rather than
Bayesian probability, simply because they have been taught to
shun subjectivity. But when it comes to making a prediction,
the Bayesian approach rules, says Marcus Appleby, a mathema­
tician at the University of London, who credits Fuchs with con­
vincing him of the significance of Bayesian probability.
Appleby points out that we would consider it crazy to bet in a
lottery after learning that the same person has won it every week
for 10 years, even though a strict frequentist would argue that
the results of prior draws have no effect on future outcomes. In
practice, no one would ignore the outcome of the previous
Asserting that
Schrödinger’s cat is
truly both alive and
dead is an absurdity,
a megalomaniac’s de­­lusion
that one’s personal state
of mind makes the world
come into being.
these lights is an addition to Bayesian probability, not in the
sense of a supplier of some kind of more-objective probabilities,
but in the sense of giving extra rules to guide the agent’s behav­
ior when he interacts with the physical world,” Fuchs writes.
The simplicity of the new equation is striking. Except for
one tiny detail, it resembles the law of total probability, the log­
ical requirement that the probabilities for all possible out­
comes add up to unity—for example, for a coin flip, the proba­
bility of landing on heads (½) plus the probability of landing on
tails (½) must equal 1. The deviant detail—the one and only ref­
erence to quantum mechanics in this prescription for how to
calculate probabilities in quantum theory—is the appearance
of d, the quantum dimension of the system. Dimension in this
sense does not refer to length or width but to the number of
states a quantum system can occupy. For instance, a single elec­
tron that can either have spin up or spin down would have a
quantum dimension of 2.
Fuchs points out that quantum dimension is an intrinsic,
irreducible attribute that characterizes the “quantum nature” of
a system, in the same way that the mass of an object characteriz­
es its gravitational and inertial properties. Although d i s implicit
in all quantum-mechanical calculations, its explicit, prominent
appearance in a fundamental equation is unprecedented. With
the Born rule in its new coat, Fuchs hopes to have discovered the
key to a new perspective on quantum mechanics. “I toy,” he con­
fesses, “with the idea of [the Born rule] being the most signifi­
cant ‘axiom’ of all for quantum theory.”
A NEW REALITY
weeks. Instead the commonsense move would be to adopt the
Bayesian viewpoint, update our knowledge and act according to
the best available evidence.
rewriting QUANTUM RULES
Although QBism negates the reality of the wave function, it is
not some nihilistic theory that negates all reality, emphasizes
QBism co-author Schack. The quantum system examined by an
observer is indeed very real, he notes. Philosophically, Mermin
says, QBism suggests a split or boundary between the world in
which the observer lives and that person’s experience of that
world, the latter described by a wave function.
Mathematically, Fuchs recently made an important discovery
that could help cement QBism’s stake as a valid interpretation of
probability and quantum theory. The finding has to do with the
empirical formula, known as the Born rule, which tells observers
how to calculate the probability of a quantum event using the
wave function. (In technical terms, the Born rule says that we
can measure the likelihood of finding a quantum system with
property X by taking the square of the magnitude of the wave
function assigned to X.) Fuchs demonstrated that the Born rule
could be rewritten almost entirely in terms of the language of
probability theory, without referring to a wave function. The
Born rule used to be the bridge that connected wave functions to
the results of experiments; now Fuchs has shown that we can
predict the results of experiments using probabilities alone.
For Fuchs, the new expression of the Born rule provides
another hint that the wave function is just a tool that tells
observers how to calculate their personal beliefs, or probabili­
ties, about the quantum world around them. “The Born rule in
One of the criticisms of QBism is that it is unable to explain
complex macroscopic phenomena in terms of more primitive
microscopic ones in the way that conventional quantum me­­
chanics does. The most direct way of meeting that challenge is
for QBism to succeed in its stated aim of building the standard
theory of quantum mechanics on a foundation of new, compel­
ling assumptions.
That goal has yet to be reached, but even now QBism offers a
new view of physical reality. By interpreting the wave function as
personal degrees of belief, it gives precise, mathematical meaning
to Bohr’s intuition that “physics concerns what we can say about
nature.” And proponents of QBism embrace the notion that until
an experiment is performed, its outcome simply does not exist.
Before the speed or position of an electron is measured, for
example, the electron does not have a speed or a position. The
measurement brings the property in question into being. As
Fuchs puts it, “With every measurement set by an experimenter’s
free will, the world is shaped just a little as it participates in a
kind of moment of birth.” In this way, we become active contrib­
utors to the ongoing creation of the universe. more to explore
Quantum Mechanics: Fixing the Shifty Split. N. David Mermin in Physics Today, Vol. 65, No. 7, page 8; July 2012.
Interview with a Quantum Bayesian. Christopher A. Fuchs. http://arxiv.org/abs/
1207.2141
QBism, the Perimeter of Quantum Bayesianism. Christopher A. Fuchs. http://arxiv.org/
abs/1003.5209
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